A slab X of thickness 't', thermal conductivity 'K' and area of cross-section 'A' is placed in thermal contact with another slab Y which is 2n2 times thicker, 4n times conductive and having n times larger cross section area. If the outside face of X is maintained at 100° C, the outside face of Y at 0° C, then the temperature (.t.) of the junction is represented by the graph (.n0.) :

Question

A slab X of thickness 't', thermal conductivity 'K' and area of cross-section 'A' is placed in thermal contact with another slab Y which is 2n2 times thicker, 4n times conductive and having n times larger cross section area. If the outside face of X is maintained at 100° C, the outside face of Y at 0° C, then the temperature (.t.) of the junction is represented by the graph (.n>0.) : (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

At equilibrium: overset⋅ Q1= overset⋅ Q2 ⇒ (K A (. t - 0 .)/ℓ )=(4 n k A n (. 100 - t .)/2 n2 ℓ ) ⇒ t=(200/3)° C

At equilibrium: Q⋅​1​=Q⋅​2​ ⇒ℓKA(t−0)​=2n2ℓ4nkAn(100−t)​ ⇒t=3200​∘C

At equilibrium: $Q \cdot_{1} = Q \cdot_{2}$
$\Rightarrow \frac{K A ( t - 0 )}{ℓ} = \frac{4 nk A n ( 100 - t )}{2 n ^{2} ℓ}$
$\Rightarrow t = \frac{200}{3}^{\circ} C$